Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

Li, Fan; Tong, Guangyu

doi:10.1002/bimj.202000230

Cited by 15 publications

(28 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has been an extensive effort in studying the impact of unequal cluster sizes in CRTs on the estimation and inference of the average treatment effect; see, for example, Kerry et al 10 and van Breukelen et al 11 with a continuous outcome; Candel et al, 12 Li and Tong 13 for a binary outcome; Li and Tong 14 for a count outcome. The consensus from these prior investigations is that the impact of cluster size variability depends on the choice of analysis.…”

Section: Discussionmentioning

confidence: 99%

“…The mean cluster size is chosen to be

\overset{true‾}{m} \in {20, 50, 100}

, and the degree of cluster size variation is chosen to be

CV \in {0, 0.3, 0.6, 0.9}

. These values are in accordance with previous simulations of CRTs with unequal cluster sizes 13,14 . When the effect modifier is continuous, the marginal covariate variance,

σ_{x}^{2}

, is set to 1, and the true HTE parameter,

β_{4} = δ

, is among

{0.10, 0.15, 0.25}

.…”

Section: Simulation Studymentioning

confidence: 94%

“…A systematic review conducted by Eldridge et al 9 indicated two‐thirds of CRTs have unequal sized clusters. The impact of unequal cluster sizes for the average treatment effect analysis has been investigated in, for example, Kerry et al, 10 van Breukelen et al, 11 Candel and van Breukelen, 12 and Li and Tong; 13,14 a good review can also be found in Eldridge et al 15 These authors found that while cluster size variation can lead to a notable loss of efficiency or power for cluster‐level analyses, 10 they lead to smaller loss of efficiency in CRTs with linear mixed model analyses 11 . In most cases, the loss of power is compensated for by the addition of 10% to 14% more clusters, depending on the magnitude of variation in cluster sizes 11,12 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accounting for unequal cluster sizes in designing cluster randomized trials to detect treatment effect heterogeneity

Tong

Esserman

2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

Unequal cluster sizes are common in cluster randomized trials (CRTs). While there are a number of previous investigations studying the impact of unequal cluster sizes on the power for testing the average treatment effect in CRTs, little is known about the impact of unequal cluster sizes on the power for testing the heterogeneous treatment effect (HTE) in CRTs. In this work, we expand the sample size procedures for studying HTE in CRTs to accommodate cluster size variation under the linear mixed model framework. Through analytical derivation and graphical exploration, we show that the sample size for the HTE with an individual‐level effect modifier is less affected by unequal cluster sizes than with a cluster‐level effect modifier. The impact of cluster size variability jointly depends on the mean and coefficient of variation of cluster sizes, covariate intraclass correlation coefficient (ICC) and the conditional outcome ICC. In addition, we demonstrate that the HTE‐motivated analysis of covariance framework can be used for analyzing the average treatment effect, and offer a more efficient sample size procedure for studying the average treatment effect adjusting for the effect modifier. We use simulations to confirm the accuracy of the proposed sample size procedures for both the average treatment effect and HTE in CRTs. Extensions to multivariate effect modifiers are provided and our procedure is illustrated in the context of the Strategies to Reduce Injuries and Develop Confidence in Elders trial.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The mean cluster size is chosen to be

\overset{true‾}{m} \in {20, 50, 100}

, and the degree of cluster size variation is chosen to be

CV \in {0, 0.3, 0.6, 0.9}

. These values are in accordance with previous simulations of CRTs with unequal cluster sizes 13,14 . When the effect modifier is continuous, the marginal covariate variance,

σ_{x}^{2}

, is set to 1, and the true HTE parameter,

β_{4} = δ

, is among

{0.10, 0.15, 0.25}

.…”

Section: Simulation Studymentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accounting for unequal cluster sizes in designing cluster randomized trials to detect treatment effect heterogeneity

Tong

Esserman

2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

show abstract

“…As pointed out by the reviewers, unequal cluster sizes occur very common in real‐world CRTs. Many researchers, including our team, have investigated on how to incorporate varying cluster size into the sample size estimation by using the coefficient of variation of cluster size for different types of cluster randomization design 26,45‐47 . We expect similar results for matched‐pair CRTs with missing binary outcomes, which is an interesting topic for future research.…”

Section: Discussionmentioning

confidence: 71%

Sample size considerations for matched‐pair cluster randomization design with incomplete observations of binary outcomes

Zhu

Hoang

et al. 2021

Statistics in Medicine

View full text Add to dashboard Cite

Multiple public health and medical research studies have applied matched‐pair cluster randomization design to the evaluation of the intervention and/or prevention effects. One of the most common and severe problems faced by researchers when conducting cluster randomized trials (CRTs) is incomplete observations, which are associated with various reasons causing the individuals to discontinue participating in the trials. Although statistical methods to remedy the problems of missing data have already been proposed, there are still methodological gaps in research concerning the determination of sample size in matched‐pair CRTs with incomplete binary outcomes. One conventional method for adjusting for missing data in the sample size determination is to divide the sample size under complete data by the expected follow‐up rate. However, such crude adjustment ignores the impact of the structure and strength of correlations regarding both outcome data and missing data mechanism. This article provides a closed‐form sample size formula for matched‐pair CRTs with incomplete binary outcomes, which appropriately accounts for different missing patterns and magnitudes as well as the effects of matching and clustering on the outcome and missing data. The generalized estimating equation (GEE) approach treats incomplete observations as missing data in a marginal logistic regression model, which flexibly accommodates various types of intraclass correlation, missing patterns, and missing proportions. In the presence of missing data, the proposed GEE sample size method provides higher accuracy as compared with the conventional method. The performance of the proposed method is assessed by simulation studies. This article also illustrates how the proposed method can be used to design a real‐world matched‐pair CRT to examine the effect of a team‐based approach on controlling blood pressure (BP).

show abstract

“…Alternatively, one may pre-specify the primary analysis to be the GEE analysis with an independence working correlation and account for clustering simply via the sandwich variance. In a two-level design with equal cluster sizes, previous studies (Pan, 2001;Li and Tong, 2021) have found that GEE estimators with working exchangeable and working independence have the same asymptotic efficiency when the randomization is carried out at the cluster level (i.e. the highest level in a two-level design).…”

Section: Considerations On Using An Independence Working Correlationmentioning

confidence: 97%

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials

Wang¹,

Turner²,

Preisser³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in health care research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multi-level CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as 8 clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanced designs.

show abstract

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

Cited by 15 publications

References 52 publications

Accounting for unequal cluster sizes in designing cluster randomized trials to detect treatment effect heterogeneity

Accounting for unequal cluster sizes in designing cluster randomized trials to detect treatment effect heterogeneity

Sample size considerations for matched‐pair cluster randomization design with incomplete observations of binary outcomes

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials

Contact Info

Product

Resources

About